On the first 5 quizzes of her physics class, Nadia got an average score of 87. What does she need on the next quiz to have an overall average of 89?
Let her score on the next quiz be $x$ The sum of all of her scores is then $5 \cdot 87 + x$ The same sum must also be equal to $6 \cdot 89$ Solve: $x = 6 \cdot 89 - 5 \cdot 87 = 99$.